It's 29 years since I last went on a family holiday. I was 11 and spent most of it sulking in the back of a car in France, soaking up an atmosphere of simmering resentment. I haven't missed them much, but you get a husband, have a baby – what can you do? All I knew was that I didn't want to spend my next one sulking in a car. I wanted somewhere warm, with more to see than dispiriting rows of sun loungers, that respected adults while catering for toddlers.

Lanzarote may not seem the obvious choice, but flee its flop-and-drop resorts for the north and this Canary Island comes into its own. We stayed near Arrieta, a crisp, white fishing village crisscrossed with cobbled alleyways next to the clean sand of La Garita beach.

While Arrieta felt traditional, a throwback to pre-package-holiday days, the retreat where we stayed was unique. Finca de Arrieta started as a tumbledown farm and grew with its owners, Michelle and Tila Braddock. They renovated the farmhouse and barns, moving from one to the other as their family expanded, letting the properties they'd outgrown. A guest suggested that a yurt would make a useful extra bedroom and that really set the ball rolling. The property now comprises 11 self-catering properties, a mix of buildings and luxury yurts, all off-grid, with a communal veranda and two large sunken water tanks serving as splash pools. The yurts come with kitchens and bathrooms so you can pretend to impressionable children that you're camping yet still enjoy a massive double bed and cook with a fully fitted oven.

Alice and Robin by their yurt in Lanzarote. Photograph: Observer

You won't know how great the Finca is unless you have kids. My daughter thinks 6am is a lie-in. That's at least four hours to fill before any shop, café or tourist attraction opens. I don't know what I'd have done without Molly the donkey, the clutch of chickens and the children's playground at the Finca. No one wants to be on a trampoline as the sun rises but as the alternative was staring into her adorable, shouting, bored face, most mornings I could have kissed its coiled steel springs.

This was all amazing, but not enough. I get as irked as a toddler without some cultural distraction. And this was where Lanzarote really surprised me. The island has fascinating landmarks thanks to the vision of one man. Local artist and architect César Manrique loved Lanzarote and dedicated his life to preserving its natural volcanic charm. His influence on planning regulations from the late 60s onwards has kept the island's resorts low rise and their architecture close to traditional styles. He also designed facilities at many key attractions, mainly in the late 60s to early 70s, and his take on luxury tourism that respects the environment is remarkable.

Lanzarote is a Unesco-designated biosphere reserve and has many sites of great, unusual beauty, such as the Mirador del Río lookout post in the Famara mountains, the volcanic wastelands in Timanfaya national park and Jameos del Agua's surreal underground lake, part of a vast lava tube. These have all been augmented with Manrique's equally stunning manmade additions – grand concert auditoriums, swimming pools and restaurants.

Camp it up: a luxury yurt at Finca de Arrieta. Photograph: Ronn Ballantyne

While the architecture works with Lanzarote's rather severe landscape, the interiors are all about Manrique. They are beautifully preserved time-warp examples of 1960s modern design, full of leather banquettes, picture windows and abstract metal sculptures. You will not visit a more elegant sightseers' café than that at Mirador del Río. Even changing a nappy felt slightly sophisticated when done in the toilets at El Diablo, the restaurant Manrique designed in Timanfaya. The architect built his own home in Tahíche in 1968, based around a series of five subterranean lava bubbles, and it looks like the sort of place that Dr No would have come to work on his tan. The building now houses the César Manrique Foundation, which continues his conservation work, and a rather excellent art collection.

What I thought would be a limp compromise was a revelation. Family isn't such an impediment to a good time after all. Especially if you go to Lanzarote. From the moment you arrive, the island's sun, sand and sea shouts holiday, but there are also many subtler, more unexpected sights and experiences to be had on its peculiar craggy shores. Go. You simply won't have time to sulk.

Essentials

Alice Fisher travelled courtesy of the Lanzarote Tourist Board and stayed at Finca de Arrieta (lanzaroteretreats.com), where yurts cost from £495 per week. Monarch has flights to Lanzarote from Birmingham, East Midlands, Gatwick, Luton, Leeds, Bradford and Manchester from £145 return including taxes (monarch.co.uk). More details on Lanzarote at turismolanzarote.com/en